Estimation of P{X < Y} for gamma exponential model

Abstract

In this paper, we estimate probability P{X &lt; Y} when X and Y are two independent random variables from gamma and exponential distribution, respectively. We obtain maximum likelihood estimator and its asymptotic distribution. We perform some simulation study.

On estimation of high quantiles for certain classes of distributions

“…X can be model with Gamma(1,152.5) distribution. Jovanović and Rajić [9] studied validity of the Gamma distribution for that data and they computed Kolmogorov-Smirnov (KS) distance between the empirical distribution function and the fitted distribution function, and KS statistic is approximately 0.23 with p value grater than 0.05. It is clear that the Gamma model fits quite well this data set.…”

Stress-Strength Reliability Model with The Exponentiated Weibull Distribution: Inferences and Applications

“…Due to the practical importance, the estimation of R has attracted the attention of several authors who considered several distributions such as exponential, normal, Weibull, generalized exponential etc.. Among of other works deal with inferences about R: Mahdizadeh (2018), Sarhan et al (2015), Rao et al (2016), Jovanovic and Rajic (2014), Raqab et al (2008), Weerahndi and Johnson (1992), Constantine et al (1986), Rezaei et al (2010). Our aim in this research is to focus on inferences for R = P(Y < X) when X and Y are two independent but not identical distributed random variables with the exponentiated Weibull (EW) distribution.…”

Bayes Estimation of Augmenting Gamma Strength Reliability of a System under Non-informative Prior Distributions

“…[9] and Jovanovic and Rajic. [10] In this article, we assume that the stress (Y) and strength (X) are independent and identically distributed random variables which follow two-parameter gamma distribution with scale parameter α and shape parameter λ, and the probability density function (pdf) of X (or Y) is given by ; x 0, , 0.…”